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SIGNS AND GRAPHS OF TRIGONOMETRIC FUNCTIONS

Introduction

As done in coordinate geometry, the coordinate axes divide the coordinate plane into four quadrants. They are named as I quadrant, II quadrant, III quadrant and IV quadrant.

Now we will learn about the pattern of trigonometric ratios:We have six trigonometric ratios:Sine (Sin), Cosine (Cos), Tangent (Tan), Cosecant (Cosec), Secant (Sec), Cotangent (Cot)We will discuss about trigonometric function in detail using Unit Circle:

Signs of Trigonometric Functions

Now we will discuss about the signs of trigonometric ratios in different quadrant.

I quadrant

I quadrant lies between the coordinates A (1, 0) and B (0, 1).Also, in the first quadrant (0 < x< Π2) a and b are both positive.So, in I quadrant – All trigonometric ratios are positive.

II quadrant

II quadrant lies between the coordinates B (0, 1) and C (-1, 0) In II quadrant (Π2 < x < Π) a is negative and b is positive. So, in II quadrant – Sine and Cosecant are positive rest all are negative.

III quadrant

III quadrant lies between the coordinates C (-1, 0) and D (0, -1)In III quadrant (Π < x < 3Π2) a and b both are negative.So, in III quadrant – Tangent and Cotangent are positive rest all are negative.

IV quadrant

IV quadrant lies between the coordinates D (0, -1) and A (1, 0)In IV quadrant (3Π2< x < 2Π) a is positive and b is negative.So, in IV quadrant – Cosine and Secant are positive rest all are negative.Important Remark:We have a simple aid to memorise the signs of trigonometric ratios in different quadrants.ALL SCHOOL TO COLLEGEI II III IV• Letter ‘A’ states that all trigonometric ratios are positive in the I quadrant.• Letter ‘S’ states that only Sine and its reciprocal are positive in the II quadrant.• Letter ‘T’ states that only Tangent and its reciprocal are positive in the III quadrant.• Letter ‘C’ states that only Cosine and its reciprocal are positive in the IV quadrant.

Graphs of Trigonometric Functions

The above table is based on the observations of different trigonometric ratios in respective quadrants.From this, we can have the graphs of each trigonometric ratio mentioned in the above table.1. Sin x

2. Cos x

3. Tan x

4. Cosec x

5. Sec x

6. Cot x

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